Some results on Horadam quaternions

Elif Tan, Ho Hon Leung

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)


In this work, we present some matrix representations associated with the Horadam quaternions which are defined by Wn=wn+wn+1i+wn+2j+wn+3k, where the components are taken from the Horadam sequence {wn}. We derive many identities related to them by using the matrix technique which is more practical. Since various well-known Fibonacci-type quaternion matrices are special cases of Horadam quaternion matrices, we have a unified way of dealing with many special quaternion sequences in the literature. As an application, we derive some binomial-sum identities.

Original languageEnglish
Article number109961
JournalChaos, Solitons and Fractals
Publication statusPublished - Sept 2020


  • Fibonacci quaternions
  • Horadam quaternions
  • Matrix method
  • Quaternions

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • General Mathematics
  • General Physics and Astronomy
  • Applied Mathematics


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